The SSD has recently been developed as an alternate to the hard disk. This memory device uses a NAND flash memory as the storage medium, and adopts a write once method and an address translation method of translating a logical address to a physical address. To reduce the free spaces and save the capacity, this memory device executes write data move processing. When data move processing and user data write to the same logical address are performed in parallel, the position of latest data recorded in the address translation table is lost. To avoid this, the user data write waits in such a case.